Forming limit of electrodeposited nickel coating in the left region

A uniform nickel (Ni) coating was bilaterally electrodeposited on the low-carbon steel substrate for the application of advanced battery shells. Its forming limit was investigated by Hill localized necking theory coupled with finite element simulation and scanning electron microscopy. The effective stress and effective strain in the Ni coating and steel substrate are deduced using Hill’s anisotropic yield function. The localized necking condition is derived by sandwich sheet analysis, and the forming limit strains are obtained by solving the nonlinear equation of the localized necking condition. Extensive calculations are carried out using the proposed model. This study exhibits the nickel coating thickness and the normal anisotropic coefficients of the coating and substrate have little influence on the forming limit curve (FLC) in the left region of the coated sheet, but the strain hardening exponents of the coating and substrate have much effect on it. The calculated result matches well with the measured data in uniaxial tension. This investigation is useful for the preparation of the electrodeposited Ni coating and helpful for the forming operation of the battery shells.     

Analytical and experimental investigations on deformation mechanism and fracture behavior in single point incremental forming

Incremental sheet forming (ISF) is a highly versatile and flexible process for rapid manufacturing of complex sheet metal parts. The characteristic of localized deformation is significantly different from conventional sheet metal forming process. To understand the fundamental material deformation mechanism during the ISF process is of great importance for ISF process design and optimization in achieving improved material formability, accuracy and more uniform thickness distribution. In this paper, an analytical model for single point incremental forming (SPIF) process has been developed to describe the localized deformation mechanism. With the consideration of both bending effect and strain hardening, the stress and strain states in the deformation zone are described. Analytical evaluation reveals that the deformation occurs not only in the contact zone, but also in the neighboring wall which has been already formed in the vicinity of the contact zone. In addition, the results also suggest that the fracture tends to appear at the transitional zone between the contact area and the formed wall. In order to validate the analytical results, SPIF simulation and experiments both have been conducted with good agreement obtained.     

Analysis of plastic flow localization under strain paths changes and its coupling with finite element simulation in sheet metal forming

Formability of sheet metal is usually assessed by the useful concept of forming limit diagrams (FLD) and forming limit curves (FLC) represent a first safety criterion for deep drawing operations. The level of FLC is strongly strain path dependent as observed by experimental and numerical results and therefore non-proportional strain paths need to be incorporated when analyzing formability of sheet metal components. Simulations using finite element method allow accurate predictions of stress and strain distributions in complex stamped parts. However, the prediction of localized necking is a difficult task and the combination of forming limit diagram analysis with finite element simulations often fail to give the right answer, if complex strain paths are not included in these predictions.     

Numerical Investigations on the Influence of Superimposed Double-Sided Pressure on the Formability of Biaxially Stretched AA6111-T4 Sheet Metal

Lightweight materials have been widely used in aerospace, automobile industries to meet the requirement of structural weight reduction. Due to their limited plasticity at room temperature, however, lightweight materials always exhibit distinctly poor forming capability in comparison with conventional deep drawing steels. Based on the phenomenon that the superimposed hydrostatic pressure can improve the plasticity of metal, many kinds of double-sided pressure forming processes have been proposed. In the present study, the Gurson-Tvergaard-Needleman (GTN) damage model combined with finite element method is used to investigate the influence of double-sided pressure on the deformation behavior of biaxially stretched AA6111-T4 sheet metal, including nucleation and growth of microvoids, evaluation of stress triaxiality, and so forth. The Marciniak-Kuczynski (M-K) localized necking model is used to predict the right-hand side of the forming limit diagram (FLD) of sheet metal under superimposed double-sided pressure. It is found that the superimposed double-sided pressure has no obvious effect on the nucleation of microvoids. However, the superimposed double-sided pressure can suppress the growth and coalescence of microvoids. The forming limit curve (FLC) of the biaxially stretched AA6111-T4 sheet metal under the superimposed double-sided pressure is improved and the fracture locus shifts to the left. Furthermore, the formability increase value is sensitive to the strain path.     

Evaluation of effect of flow stress characteristics of tubular material on forming limit in tube hydroforming process

The material properties for the analytical and numerical simulation in sheet metal processes, especially in tube hydroforming process, are generally obtained from the uniaxial tensile test of raw sheet material. However, the validation of the formability and reliability of the numerical simulation for the tube hydroforming process arises from the fact that the material characteristics of tubes are different from those of the raw sheet materials. In order to determine the most suitable material property of the tubular material for the evaluation of forming limit on the THF process, the uniaxial tensile test for the specimens of the raw sheet metal and the roll-formed tube and the free bulge test for the roll-formed tubular material are carried out in this paper. The forming limit curves are also derived using plastic instability based on three kinds of necking criteria, which are Hill’s local necking criterion for sheet and Swift’s diffuse necking criteria for sheet and tube, to describe and explain the forming limits for the roll-formed tubular material in the THF process. In order to acquire the informative data on the forming limit curves in the THF process, the loading condition of the free bulge test is controlled. The proper band from nearly necking initiation to nearly bursting initiation has been defined for the roll-formed tubular material in the THF process. It can be concluded that the flow stress of the tubular material should be determined from the actual free bulge test to find the practically valuable forming limit curve for the THF process.     

A geometrical model of the kinematics of incremental sheet forming for the prediction of membrane strains and sheet thickness

The sine law is a simple geometrical model for incremental sheet metal forming (ISF). It is based on the assumption that the deformation is a projection of the undeformed sheet onto the surface of the final part. The sine law provides approximations of sheet thinning for shear spinning and ISF at negligible computational cost, but as a plane strain model it can be applied only when plane strain deformation prevails.     

Formability limits by fracture in sheet metal forming

The aim of this paper is twofold: first, to revisit the forming limit diagram (FLD) in the light of fundamental concepts of plasticity, damage and ductile fracture mechanics and, second, to propose a new experimental methodology to determine the formability limits by fracture in sheet metal forming. The first objective makes use of the theory of plasticity applied to proportional strain loading paths, under plane stress conditions, to analyze the fracture forming limit line (FFL) and to introduce the shear fracture forming limit line (SFFL). The second objective makes use of single point incremental forming (SPIF), torsion and plane shear tests to determine the experimental values of the in-plane strains at the onset of fracture. Results show that the proposed methodology provides an easy and efficient procedure to characterize the formability limits by fracture in sheet metal forming. In particular, the paper shows that the FFL determined by means of tensile and conventional sheet formability tests is identical to that determined from SPIF tests on conical and pyramidal truncated specimens. The new proposed approach is expected to have impact in the established methodologies to outline the formability limits on the basis of the forming limit curves (FLC's) at the onset of necking.     

Multi-pass deformation design for incremental sheet forming: Analytical modeling,finite element analysis and experimental validation

Incremental sheet forming (ISF) is a promising rapid prototyping technology with high potential to shape complex three-dimensional parts. However, a common technical problem encountered in ISF is the non-uniform thickness distribution of formed parts; particularly excessive thinning on severely sloped regions. This may lead to fracture and limit the process formability. Design of multi-stage deformation passes (intermediate shapes or preforms) before the final part, is a desirable and practical way to control the material flow in order to obtain a more uniform thickness distribution and avoid forming failure. In the present paper, a systematic methodology for designing multi-stage deformation passes considering the predicted thickness strains given the design shape is proposed based on the shear deformation and the strain compensation mechanism. In this methodology, two analytical models (M1 and M2) are developed by taking into account; the global average thickness strain and only the material in the final part region used in the forming (M1), and the local weighted average thickness strain and the additional material around the final part region used in the forming (M2), respectively. The feasibility of the proposed design methodology is validated by finite element analysis (FEA) and experimental tests using an Amino ISF machine. The results show that a more uniform thickness strain distribution can be derived using M2. The incurrence of the highest strains can be delayed in the intermediate stages and the flow of material is allowed into the deformed region, thereby allowing a compressive stress state to develop and enabling steeper shapes to be formed. Therefore, the process formability can be enhanced via the optimized design of deformation passes.     

Mechanism investigation of friction-related effects in single point incremental forming using a developed oblique roller-ball tool

Single point incremental forming (SPIF) is a highly versatile and flexible process for rapid manufacturing of complex sheet metal parts. In the SPIF process, a ball nose tool moves along a predefined tool path to form the sheet to desired shapes. Due to its unique ability in local deformation of sheet metal, the friction condition between the tool and sheet plays a significant role in material deformation. The effects of friction on surface finish, forming load, material deformation and formability are studied using a newly developed oblique roller ball (ORB) tool. Four grades of aluminum sheet including AA1100, AA2024, AA5052 and AA6111 are employed in the experiments. The material deformation under both the ORB tool and conventional rigid tool are studied by drilling a small hole in the sheet. The experimental results suggest that by reducing the friction resistance using the ORB tool, better surface quality, reduced forming load, smaller through-the-thickness-shear and higher formability can be achieved. To obtain a better understanding of the frictional effect, an analytical model is developed based on the analysis of the stress state in the SPIF deformation zone. Using the developed model, an explicit relationship between the stress state and forming parameters is established. The experimental observations are in good agreement with the developed model. The model can also be used to explain two contrary effects of friction and corresponding through-the-thickness-shear: increase of friction would potentially enhance the forming stability and suppress the necking; however, increase of friction would also increase the stress triaxiality and decrease the formability. The final role of the friction effect depends on the significance of each effect in SPIF process.     

Two-Point Incremental Forming with Partial Die: Theory and Experimentation

This paper proposes a new level of understanding of two-point incremental forming (TPIF) with partial die by means of a combined theoretical and experimental investigation. The theoretical developments include an innovative extension of the analytical model for rotational symmetric single point incremental forming (SPIF), originally developed by the authors, to address the influence of the major operating parameters of TPIF and to successfully explain the differences in formability between SPIF and TPIF. The experimental work comprised the mechanical characterization of the material and the determination of its formability limits at necking and fracture by means of circle grid analysis and benchmark incremental sheet forming tests. Results show the adequacy of the proposed analytical model to handle the deformation mechanics of SPIF and TPIF with partial die and demonstrate that neck formation is suppressed in TPIF, so that traditional forming limit curves are inapplicable to describe failure and must be replaced by fracture forming limits derived from ductile damage mechanics. The overall geometric accuracy of sheet metal parts produced by TPIF with partial die is found to be better than that of parts fabricated by SPIF due to smaller elastic recovery upon unloading.     

DEPENDENCE OF PREDICTION MODEL OF FORMING LIMIT STRAINS ON FORMING METHOD AND MECHANICAL PROPERTIES OF SHEET METALS

ＤＥＰＥＮＤＥＮＣＥＯＦＰＲＥＤＩＣＴＩＯＮＭＯＤＥＬＯＦＦＯＲＭＩＮＧＬＩＭＩＴＳＴＲＡＩＮＳＯＮＦＯＲＭＩＮＧＭＥＴＨＯＤＡＮＤＭＥＣＨＡＮＩＣＡＬＰＲＯＰＥＲＴＩＥＳＯＦＳＨＥＥＴＭＥＴＡＬＳ①ＺｈｏｕＷｅｉｘｉａｎＤｅｐａｒｔｍｅｎｔｏｆＡｅ...     

Investigation on deformation behavior of sheet metals in viscous pressure bulging based on ESPI

In order to analyze the effect of viscous medium on the deformation behavior of sheet metals in viscous pressure bulging (VPB), the entire deformation process including instability and fracture was investigated real-timely by the aid of electronic speckle pattern interferometry (ESPI). Images of speckle patterns were captured continuously to obtain fringe patterns representing the full field strain rate. Values of strain rates were calculated based on the fringe patterns. The evolution of the weak region from the initial defect to the groove until crack was also observed through the fringe patterns. The onset of diffuse and localized necking were determined qualitatively and quantitatively. Experimental results show that the deformation of sheet metals in VPB passed through five states, namely, uniform deformation, strain localization, diffuse necking, localized necking and fracture. A defect emerged in strain localization. The growth of the defect caused the diffuse necking and generated a groove. The groove expanded mainly in length direction until the localized necking occurred. Finally the specimen fractured as a result of groove deepening. The tangential adhesive stress provided by viscous medium in VPB restricted the locally larger strain of the specimen. The diffuse necking was postponed greatly. Theoretical prediction of the limit strains of sheet metals in VPB would be made based on the experimental results in further work.     

Prediction of shear-induced fracture in sheet metal forming

Necking has been the dominant failure mode in sheet metal forming industry and several analytical and numerical tools were developed to predict the onset of necking. However, the introduction of Advanced High Strength Steels (AHSS) with reduced ductility brought up an issue of a shear fracture which could not be predicted using the concept of Forming Limit Curve (FLC). The Modified Mohr-Coulomb fracture criterion (MMC) was recently shown to be applicable to problems involving ductile fracture of materials and sheets. In the limiting case of plane stress, the fracture locus consists of four branches when represented on the plane of the equivalent strain to fracture and the stress triaxiality. A transformation of above 2D fracture locus to the space of principal strains was performed which revealed the existence of two new branches not extensively studied before. The existence of those branches explains the formation of shear-induced fracture. As an illustration of this new approach, initiation and propagation of cracks is predicted and compared with series of deep-drawing punch tests of ThyssenKrupp AHSS (grade RA-K 40/70, standard HCT690T) performed at ThyssenKrupp. It was shown that the location of fracture as well as the magnitude of punch travel corresponding to first fracture was correctly predicted by MMC fracture criterion for both circular and square punch.     

Investigation of material deformation mechanism in double side incremental sheet forming

Double side incremental forming (DSIF) is an emerging technology in incremental sheet forming (ISF) in recent years. By employing two forming tools at each side of the sheet, the DSIF process can provide additional process flexibility, comparing to the conventional single point incremental forming (SPIF) process, therefore to produce complex geometries without the need of using a backing plate or supporting die. Although this process has been proposed for years, there is only limited research on this process and there are still many unanswered open questions about this process. Using a newly developed ISF machine, the DSIF process is investigated in this work. Focusing on the fundamental aspects of material deformation and fracture mechanism, this paper aims to improve the understanding of the DSIF process. Two key process parameters considered in this study include the supporting force and relative position between master and slave tools. The material deformation, the final thickness distribution as well as the formability under varying conditions of these two process variables are investigated. To obtain a better understanding from the experimental results, an analytical model has been developed to evaluate the stress state in the deformation zone. Using the developed model, an explicit relationship between the stress state and key process parameters can be established and a drop of stress triaxiality can be observed in the double contact zone, which explains the enhanced formability in the DSIF process. Based on the analytical and experimental investigation, the advancements and challenges of the DSIF process are discussed with a few conclusions drawn for future research.     

Prediction of forming limit curve for pure titanium sheet

Commercially pure titanium (CP Ti) has been actively used in the plate heat exchanger due to its light weight, high specific strength, and excellent corrosion resistance. However, researches for the plastic deformation characteristics and press formability of the CP Ti sheet are not much in comparison with automotive steels and aluminum alloys. The mechanical properties and hardening behavior evaluated in stress–strain relation of the CP Ti sheet are clarified in relation with press formability. The flow curve denoting true stress–true strain relation for CP Ti sheet is fitted well by the Kim–Tuan hardening equation rather than Voce and Swift models. The forming limit curve (FLC) of CP Ti sheet as a criterion for press formability was experimentally evaluated by punch stretching test and analytically predicted via Hora's modified maximum force criterion. The predicted FLC by adopting Kim–Tuan hardening model and appropriate yield function shows good correlation with the experimental results of punch stretching test.     

Forming limit diagram of auto-body steel sheets for high-speed sheet metal forming

This paper is concerned with the uniaxial tensile properties and formability of steel sheets in relation to the strain rate effect. The elongation at fracture for CQ increases at a high strain rate while the elongation at fracture for DP590 decreases slightly in relation to the corresponding value for a quasi-static strain rate. The uniform elongation and the strain hardening coefficient decrease gradually when the strain rate increases. The r-value of CQ and DP590 was measured with a high-speed camera in relation to the strain rate. The r-value is slightly sensitive to the strain rate. Static forming limit curves (FLCs) and high-speed FLCs were constructed with the aid of punch-stretch tests with arc-shaped and square-shaped specimens. In addition, a high-speed crash testing machine with a specially designed high-speed forming jig was used for the high-speed punch-stretch tests. Compared with the static FLC, the high-speed FLC of CQ is higher in a simple tension region and lower in a biaxial stretch forming region. The high-speed FLC for DP590 decreases in relation to the static FLC throughout the entire region. The elongation at fracture appears to be closely related to the simple tension region of the FLC. The shear fracture is observed from SEM images of specimens tested in the biaxial stretch forming region under the high-speed forming condition. The dimples indicating the shear fracture have elongated horseshoe shape. The high-speed FLC is lower than the static FLC in the biaxial stretch forming region because the shear fracture induces the decrease of ductility. The results confirm that the strain rate has a noticeably influence on the formability of steel sheets. Thus, the forming limit diagram of high-speed tests should be considered in the design of high-speed sheet metal forming processes.     

不锈钢覆铝板成形极限的理论分析和实验验证

在Ｈｉｌ的各向塑性异性条件下推导了不锈钢覆铝板成形极限的计算模型。在应变比为负（β＜０）的区域,根据Ｈｉｌ的局部颈缩理论推导出了复合板的局部颈缩条件式;在应变比为正（β＜０）的区域,先根据Ｓｗｉｆｔ理论推导出了复合板的扩散颈缩条件式并计算出出现扩散颈缩的应变,然后在此基础上根据修正Ｍ－Ｋ理论推导出了复合板的局部颈缩的极限应变计算式。计算结果与实验数据吻合较好,发现复合板的成形极限介于其母材之间,并随着其母材中成形性好的材料的厚比增大而提高。     

Failure During Sheared Edge Stretching

Failure during sheared edge stretching of sheet steels is a serious concern, especially in advanced high-strength steel (AHSS) grades. The shearing process produces a shear face and a zone of deformation behind the shear face, which is the shear-affected zone (SAZ). A failure during sheared edge stretching depends on prior deformation in the sheet, the shearing process, and the subsequent strain path in the SAZ during stretching. Data from laboratory hole expansion tests and hole extrusion tests for multiple lots of fourteen grades of steel were analyzed. The forming limit curve (FLC), regression equations, measurement uncertainty calculations, and difference calculations were used in the analyses. From these analyses, an assessment of the primary factors that contribute to the fracture during sheared edge stretching was made. It was found that the forming limit strain with consideration of strain path in the SAZ is a major factor that contributes to the failure of a sheared edge during stretching. Although metallurgical factors are important, they appear to play a somewhat lesser role.     

Bulging in incremental sheet forming of cold bonded multi-layered Cu clad sheet: Influence of forming conditions and bending

Bulge is a defect that causes geometrical inaccuracy and premature failure in the innovative incremental sheet forming (ISF) process. This study has two-fold objectives: (1) knowing the bulging behavior of a Cu clad tri-layered steel sheet as a function of forming conditions, and (2) analyzing the bending effect on bulging in an attempt to identify the associated mechanism. A series of ISF tests and bending analysis are performed to realize these objectives. From the cause-effect analysis, it is found that bulge formation in the layered sheet is sensitive to forming conditions in a way that bulging can be minimized utilizing annealed material and performing ISF with larger tool diameter and step size. The bending under tension analysis reveals that the formation of bulge is an outgrowth of bending moment that the forming tool applies on the sheet during ISF. Furthermore, the magnitude of bending moment depending upon the forming conditions varies from 0.046 to 10.24 N·m/m and causes a corresponding change in the mean bulge height from 0.07 to 0.91 mm. The bending moment governs bulging in layered sheet through a linear law. These findings lead to a conclusion that the bulge defect can be overcome by controlling the bending moment and the formula proposed can be helpful in this regards.     

A Comparative Study of Different Necking Criteria for Numerical and Experimental Prediction of FLCs

For sheet metal forming, the determination of the onset of localized necking directly influences the formability evaluation and construction of forming limit curves (FLCs). Several necking criteria in the literature have been proposed and widely used, however, there are some restrictions, e.g., some criteria are suitable for numerical methods but not for the experimental phase. In this study, numerical and experimental procedures are carried out to seek an appropriate necking criterion for the prediction of FLCs. This article begins with the FE modeling of the Marciniak test with ABAQUS. Based on the FE simulation, different necking criteria (global and local ones) are reviewed and analyzed in detail, and the FLCs for a 5086 aluminum sheet are constructed with these criteria. On the other hand, a quasi-static experimental Marciniak test is carried out to study the formability for this given sheet. With a chosen necking criterion, the limit strains are experimentally determined. The comparison between experimental and numerical results shows that the chosen necking criterion could be effective to numerically and experimentally evaluate the global formability of this aluminum alloy on the wide range of strain states.